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Homework Help: Banked Frictionless Curve, and Flat Curve with Friction

  1. Jun 20, 2009 #1
    1. The problem statement, all variables and given/known data
    A car of mass M = 1200 kg traveling at 40.0 km/hour enters a banked turn covered with ice. The road is banked at an angle theta, and there is no friction between the road and the car's tires.

    What is the radius r of the turn if [tex]\theta[/tex] = 20.0 degrees (assuming the car continues in uniform circular motion around the turn)?

    3. The attempt at a solution

    I believe that [tex]F_{c}[/tex] = [tex]F_{N}[/tex] sin ([tex]\theta[/tex]) = m([tex]\frac{v^{2}}{r}[/tex])

    Using this I solved for r, which is my missing variable and came up with:

    r = [tex]\frac{v^{2}}{F_{N}sin\theta}[/tex]

    Using this formula I get
    r = [tex]\frac{11.1^{2}}{9.8 sin 20}[/tex]

    but when I submitted this answer it told me the normal force is not equal to the weight of the car.

    My questions are what is the [tex]F_{N}[/tex] value and am I missing another value in my equation?
  2. jcsd
  3. Jun 20, 2009 #2


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    Homework Helper

    Break down Fn into vertical and horizontal components. You already saw that the horizontal component provides the centripetal acceleration; what does the vertical component do?
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